The Brumbies trailed by four points with about two minutes remaining when centre Tevita Kuridrani crossed for the deciding try against the Bulls.
Brumbies coach Jake White dubbed the result “the greatest win the Brumbies have ever had”.
“It’s got to be,” he said, adding man of the match George Smith backed his claim.
“I spoke to George Smith after the game and he said he’s never experienced anything like that in his life.
“We defended and defended and the law of averages told us we were going to get out of our half and have one crack at getting the win. And then it happened.”
The Brumbies faced an uphill battle before kick-off on Sunday morning.
The South African Bulls had won 22 of their past 24 matches at Loftus Versfeld and were undefeated in home finals matches.
White was still perplexed as to why the Bulls turned down repeated penalty goal options.
“They have the best goal-kicker in the whole competition (Morne Steyn) and a new hooker on who has to throw the ball into the lineout. And they decide to go for touch,” White said.
“It’s moments like that that change the whole destiny of clubs.”
On Saturday, in an all-New Zealand semi, the Chiefs beat the Crusaders 20-19 in another thriller.
The Brumbies have returned to Canberra until Wednesday when they’ll move their base to Hamilton.
The Super Rugby final will air in the UK on Sky Sports 1 from 8.30am on Saturday.
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